Exam 1: Linear Equations and Inequalities in One Variable

Two cars are 270 miles apart and travel toward each other on the same road. They meet in 3 hours. One car travels 2 mph faster than the other. What is the average speed of each car?

Solve the equation: $\frac { 1 } { 3 } x = - 10$ .

Solve the absolute value equation. $\left| \frac { 3 y + 4 } { 2 } \right| = \left| \frac { 1 } { 4 } y + 1 \right|$

Solve the absolute value inequality. Write the solution in interval notation. $4 \leq \frac { | y + 3 | } { 3 } + 3$

What is the sale price of a stereo that normally sells for $210.00 and is on sale for 25% off?

Solve the inequality. Write the answer in interval notation. $5 x \leq 10 \quad$ or $\quad 15 - x < 7$

Solve the absolute value inequality. Write the solution in interval notation. $5 \leq | 4 t - 7 |$

Solve the absolute value equation. $| 6 z - 3 | = 5$

Angles A, B, and C are the angles in a triangle. Angle B is 2 times as big as angle A, and angle C is 48° more than angle A. Find the measure of angle A in degrees.

A salesperson earns $60 a day plus 12% commission on sales over $200. If her daily earnings are $95.88, how much money in merchandise did she sell?

A thermometer used to measure the temperature of a solution in a chemistry experiment has 5 tick marks for each degree, so that each tick mark corresponds to 0.2 degrees. If a solution is measured at between 33.0 and 33.2 degrees, write an absolute value inequality that describes the true temperature t.

Let $X = \{ x \mid x < - 1 \}$ and $Y = \{ x \mid x \geq - 6 \}$ . Determine the given union. Express the answer in interval nota $X \cup Y$

The plans for a rectangular deck call for the width to be 10 feet less than the length. Sam wants the deck to have an overall perimeter of 60 feet. What should the length of the deck be?

The difference of 9 and a number is between -8 and 10. Find all such numbers.

Two numbers that differ by 19 have a sum of 53. Find the smaller of the two numbers.

Solve the inequality. Write your answer in interval notation. $26 > 3 x$ and $- 1 + 2 x \geq - 8$

Solve the absolute value equation. $4 = - 1 + \left| 2 - \frac { 1 } { 4 } w \right|$

Amy knows from reading her syllabus in intermediate algebra that the average of her chapter tests accounts for 80% (0.8) of her overall course grade. She also knows that the final exam counts as 20% (0.2) of her grade. a. Suppose that the average of Amy's chapter tests is 97%. Determine the range of grades that she would need on her final exam to get an "A" in the class. (Assume that a grade of "A" is obtained if Amy's overall average is 90% or better.) b. Determine the range of grades that Amy would need on her final exam to get a "B" in the class. (Assume that a grade of "B" is obtained if Amy's overall average is at least 80% but less than 90%.)

Which expression is equivalent to $( - y - 8 ) / x$ ?

Solve the inequality. Graph the solution set and write the solution set in interval notation. 13y + 6 > 8